1. Field of the Invention
The present invention relates to processes which make it possible to correct the effects of the spurious motions of the antenna in a synthetic antenna sonar, when the path of its physical antenna is not a perfect straight line.
2. Discussion of the Background
It is known that in a sonar the resolution is related to the dimensions of the antenna with respect to the wavelength used. This makes it possible in the case of a side-looking sonar intended for performing imaging of the bottom of the sea, in which the antenna located on the sides of the carrier vessel travels substantially along a straight line parallel to the path of the vessel and perpendicular to the direction of observation of the sonar, to use a so-called synthetic antenna system in which the signals received by the antenna at successive instants, and hence locations, are used to obtain a resolution substantially equivalent to that of a virtual antenna corresponding to the length traversed by the physical antenna during these various successive instants.
To form the various channels of such a sonar, the signals received are added together, using delays corresponding to the direction of the channel formed and to the various locations of the sensors of the antenna as a function of their position on the physical antenna and of the motion of the latter.
In the simple case where this motion is perfectly linear and constant, these delays are known. In reality the carrier vessel moves a great deal and in a very random manner. Hence, the position of the sensors during measurements is not known precisely.
The resolution .delta.y of conventional (non-synthetic) bottom-imaging side-looking sonars along the longitudinal axis parallel to the course is limited by the length L of their physical reception antenna. It is given by the formula: ##EQU1##
where .lambda. is the wavelength and R the range of the sonar. PA1 where V is the mean longitudinal speed during the N recurrences and T.sub.r the duration of a recurrence. PA1 the error in estimating .tau..sub.n, PA1 the error in estimating .tau..sub.P,n (.xi..sub.-) -.tau..sub.P,n (.xi..sub.+) caused by the error in .beta..sub.n.
The corresponding resolution of a synthetic sonar whose synthetic antenna is formed on the basis of N successive recurrences is given by the formula: ##EQU2##
The main difficulty in applying the principle of the synthetic antenna to the sonar resides in the determination of the channel formation delays. Although these delays depend only on the distance and on the direction of the sighted point for a conventional antenna, those of a synthetic antenna depend on the motion of the carrier during its duration of formation. The larger this duration of formation, that is to say the larger the number of recurrences N, this going hand in hand with the search for better resolution, the more difficult it is to determine the delays.
To determine the delays in forming the channels of the synthetic antenna, one may seek to measure the motion of the physical antenna. The best precision in this measurement is achieved by means of an inertial instrumentation unit. However, it is known from an article by L. J. Cutrona "Comparison of sonar system performance achievable using synthetic-aperture sonar techniques with the performance achievable by more conventional means" -- Journal of Acoustical Society of America, Vol. 58, No. 2, August 1975, that one is then confronted with a problem regarding the precision of the acceleration measurement.
The bias .epsilon..gamma. on the sighting axis must satisfy the following relation: ##EQU3##
We must then have .epsilon..gamma.&lt;2 10.sup.-4 m/s.sup.2 in order to obtain for example a resolution of 5 cm at a range of 350 m and at the speed of 8 knots with a sonar, were its frequency to be around 100 kHz. Such a value is compatible with the intrinsic precision of the best accelerometers, but not with a measurement on a craft whose orientation within the terrestrial gravity field is unknown. To obtain it in this case, it would be necessary to be able to measure the direction of the vertical to better than 2 10.sup.-5 rd, this being a precision which cannot realistically be obtained in such an on-board sonar system.
Various so-called autofocussing methods have been proposed to solve this difficulty, this terminology being employed since the coefficients are determined on the basis of the measurements of the signal. Among these latter are known in particular methods exploiting the crosscorrelation of the acoustic field on the antenna over two successive recurrences. When the longitudinal travel between two recurrences is smaller than half the length of the reception antenna, the field at the front end of the first recurrence is strongly correlated with the field at the back end. The length L.sub.c of the two correlated ends of the field of the antenna is then given by the formula: EQU L.sub.c =L-2.V.T.sub.r. (4)
This correlation is exploited in order to estimate the longitudinal travel I, the difference .tau. in the outward and return propagation times of the sonar pulse for one and the same point of reflection on the bottom, and the rotation .beta. of the sighting direction, between the two recurrences. An example of such a method is described in American U.S. Pat. No. 4,244,036 (Raven).
FIG. 1 makes it possible to define the notation for the parameters used. Represented therein are two successive positions 101 and 102 of the physical antenna corresponding to two recurrences n-1 and n. The axis 103 is the mean longitudinal direction, that is to say the direction parallel to the antenna, for the 2 recurrences. It is not in general identical to the direction of travel of the vessel, on account of drift.
Since the difference in the propagation times .tau. relates to two reception points located at the centre of the two correlated ends 104 and 105, the estimation errors for the three parameters are independent. The three parameters I.sub.n, .tau..sub.n and .beta..sub.n being estimated on the basis of the recurrences n-1 and n, and .theta..sub.n being the sighting direction at the centre of the reception antenna of the physical antenna at recurrence n (position 102) for a fixed point a distance R away, one obtains the channel formation delay .tau..sub.S,n (.xi.) for the synthetic antenna for the signal received at recurrence n at a point with abscissa .xi. in the reference frame of the physical antenna, by means of the recurrence relations: ##EQU4##
where .theta..sub.P,n (.xi.) is the channel formation delay for the physical antenna at the point with abscissa .xi. and where .xi..sub.- and .xi..sub.+ may depend on n, since, the speed not generally being constant, the length of the two correlated ends can vary.
The direction setting for a channel is defined in the reference frame of the physical antenna at a given recurrence, for example the central recurrence of the synthetic antenna. For this reference recurrence, the channel formation delays for the synthetic antenna are those for the physical antenna. By means of the above recursive relations, the channel formation delays for all the other sonar recurrences which are used to build the synthetic antenna are then estimated gradually. The impact of the error in estimating l generally negligible compared with those of the errors in estimating the other two parameters. Each new insertion of the recursive estimation relations generates an error in the channel formation delays, which is added to the errors of the previous iterations. Thus, the error in estimating the channel formation delay at the point with abscissa .xi..sub.- after a given number of iterations is the sum of as many independent errors, each itself being the sum of two independent components:
Calling .phi..sub..tau. and .phi..sub..beta. the standard deviations of the corresponding phase errors, the latter are obtained with the aid of the following approximate expressions: ##EQU5##
where K is the number of independent samples of the signals of the antenna of one and the same recurrence involved in the autofocussing and .rho. is equal to .mu./(1-.mu.), .mu. being the crosscorrelation coefficient.
Since in practice one seeks to maximize the speed of travel of the carrier vessel, the length of the correlated ends L.sub.c must be as small as possible and the inter-recurrence travel VTr somewhat less than the upper limit value L/2 imposed by the spatial sampling constraint of the synthetic antenna. Under these conditions, it follows from the expressions for .phi..sub..tau. and .phi..sub..beta. that it is the error in estimating the rotation which is by far the most critical.
The impact of this error on the directivity gain g of the channel formed with these estimated delays is given by the relation: ##EQU6##
Referring to the practical example described earlier, the length of the physical antenna must be around 4 m and the number of recurrences constituting the synthetic antenna around 30. In order for the loss in directivity gain to be less than the commonly sought value of 1 dB, it is necessary for .phi. to be less than 0.2 rd. If .phi..sub..tau. is neglected, the relation between .phi. and the error .sigma. in measuring the rotation is given by the formula: ##EQU7##
For a range of 350 m, the duration T.sub.r of the recurrence is 470 ms. Relation (4) then gives l.sub.c =0.3 m for L=4 m and V=8 knots. Hence, in the example described, the standard deviation in the estimation of the rotation, carried out on the basis of the antenna signals at the two ends of length L.sub.c, must be less than 10.sup.-4 rd.
The angular resolution .lambda./L.sub.c of each end is equal to 5 10.sup.-2 rd, i.e. 500 times the precision required in estimating the rotation. It is therefore unrealistic to hope to achieve such precision by estimation on the basis of the antenna signals.